ISE 426-526 - Lecture 4 - RCBD & Latin Square Designs

ISE 426-526 - Lecture 4 - RCBD & Latin Square...

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1 ISE 426/526 Lecture 4 - 2007 Randomized Complete Block Designs Latin Square Designs The Randomized Block Design Experimental Designs CRD RBD Single Factor Multiple Factors RCBD Incomplete Block Designs Single Factor Multiple Factors
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2 What is a Block? • Restriction on Randomization • Subset of material that should be more homogenous than entire set of material • Used to control a nuisance factor Comparison of RCBD & CRD RCBD CRD Table 4-1, pg. 120
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3 The Airplane Experiment II Randomized Complete Block Design The Airplane Experiment II Objective: _____________________________ Response: _____________________________ Factors: _______________________________ Nuisance Factor: ________________________
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4 Setting Up the Experiment Operator Plane Rand Run Order Results 1 1 10480 2 22368 3 24130 2 1 42167 2 37570 3 77921 3 1 99562 2 96301 3 89579 The Theoretical Model y ij = μ + τ i + β j + ε ij μ = overall mean τ i = effect of i th treatment mean β j = effect of j th Block ε ij = NID(0, σ 2 ) random error
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5 The Hypothesis Partitioning of SS Total 222 2 .. . .. . .. . . .. 11 1 1 () ( ) ab a b ij i j ij j i ij i j yy b a yyyy == = = −= −+ + ∑∑
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6 Calculation Formulas Components of ANOVA Table
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7 Airplane Experiment II – Data Total 3 2 1 Total 3 2 1 Opr\Plane Airplane Experiment II - Calculations
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8 Airplane II - ANOVA – RCBD Source df SS MS F p Operator Plane Error Total Example 4-1, pg. 124 Extrusion P r e s s u r e ( P S I ) 123456 Treatment Totals 8500 90.3 89.2 98.2 93.9 87.4 97.9 556.9 8700 92.5 89.5 90.6 94.7 87.0 95.8 550.1 8900 85.5 90.8 89.6 86.2 88.0 93.4 533.5 9100 82.5 89.5 85.6 87.4 78.9 90.7 514.6 Block Totals 350.8 359.0 364.0 362.2 341.3 377.8 2155.1 Batch of Resin (Block) Medical device manufacturer produces vascular grafts. Some of the tubes in a run develop defects. The developer suspects that the extrusion pressure affects the occurrence of defects. The engineer also suspects there maybe significant batch-to-batch variation.
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9 ANOVA Calculations Example 4-1 (cont.) Correct Analysis as RCBD
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ISE 426-526 - Lecture 4 - RCBD & Latin Square...

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